To be fair, I wouldn't say there's any harm in getting a drysuit first. I mean, once you're in a club that provides all the equipment other than a drysuit, and you know you like the sport, I can't see any difficulty in getting a drysuit before a boat or paddle.
The order in which you pick up your paddling things is something that you choose, based on your own priorities.
Obviously though, if you want to do more private trips without the hassle of borrowing gear you may want to consider looking into a boat & paddle first.